Approximation of discrete spatial data for continuous facility location design

The paper proposes methodologies to adaptively convert discrete spatial data into continuous functions in a metric space so that the continuum approximation (CA) optimization framework can be applied to a general class of discrete facility location problems. We implement a Voronoi diagram based interpolation method to estimate the optimal system cost and the optimal number of facilities, and then develop an enhanced disk model to compute near-optimum facility location design, both based on discrete input data. The results from the proposed CA method can be further improved by neighborhood search algorithms. Numerical experiments show that the proposed CA framework effectively finds near-optimum solutions to very large problem instances within a short time.